David Cameron vowed that the coalition would last the full five-year term. Photograph: Isopix/Rex Features

David Cameron has issued a blunt warning to Conservative Eurosceptics that his "very clear, very decisive policy" to hold a referendum on Britain's EU membership by the end of 2017 is not up for renegotiation.

In an attempt to draw a line under a bumpy few weeks in which Eurosceptics demanded a toughening of his policy and Tory traditionalists criticised him for pressing ahead with a gay marriage bill, the prime minister said he would stand firm.

But Cameron, who spoke of his pride in legalising gay marriage, tried to reach out to the right by saying he would now focus on the "big picture" issues of the economy rather than social issues.

"Is this the first now of many other issues like that," he asked in an interview on the Today programme on Radio 4. "No it isn't. The government now is going to be absolutely focused on the big picture which is fixing our economy, reforming welfare, making sure there are good schools for our children to go to."

But the prime minister adopted a different tone as he rejected calls from Eurosceptics to hold a referendum before the planned date of 2017, or even to hold two votes. David Davis, the former Tory leadership contender, is calling for an initial "mandate" referendum to give the prime minister authority from the British people to renegotiate the terms of Britain's EU membership.

Cameron said: "On 24 January I set out a very clear, very compelling policy for the country towards Europe, which is to renegotiate our relationship with Europe, to make the European Union more open, competitive and flexible, and then to offer the British people something they haven't had for decades – an in-out referendum. It's a very clear, very decisive policy.

"Let me say, this policy, it doesn't matter the pressure I come under from outside the Conservative party, or in Europe, or inside the Conservative party, this policy isn't going to change. The question isn't going to change. The number of referenda isn't going to change. The date by which we hold this referendum isn't going to change. The fact is, it's the right policy for the country."

The prime minister also joined forces with Nick Clegg in vowing that the coalition would last the full five-year term. He said on Today: "That is absolutely my intention and has always been. To anyone who doubts what life there is left in the coalition, I would argue there is more to come – very bold reforming, and strong government, and that is what we'll be right up until polling day."

Clegg urged the Conservatives not to shift to the right in a doomed bid to head off Ukip. The deputy prime minister warned Tory MPs off "arcane, shrill and tongue-twisting manoeuvres in parliament", saying it distracted the public from the government's main goal of sorting out the economy.

Speaking at a press conference in Westminster, Clegg told the Conservatives they were wasting their time trying to stir up a leadership crisis in his own party, but admitted long-term differences between the two parties over Europe would continue.

Insisting he was confident of his place in the coalition, he said: "Anyone who is wargaming about what may or may not happen in my party is wasting their time. I am going to be leader of this party up to, through and beyond the next general election. The Liberal Democrats, despite all the predictions to the contrary, have proved to be the calmest, most resilient and most united party in British politics today."